Asymptotics for Two-dimensional Atoms

Details Asymptotics for Two-dimensional Atoms Asymptotics for Two-dimensional Atoms

2011-02-21

arxiv.org/abs/1102.4229v2

Physics

Mathematical Physics

Revised version to appear in Ann. Henri Poincar\'e

Scientific paper

We prove that the ground state energy of an atom confined to two dimensions with an infinitely heavy nucleus of charge $Z>0$ and $N$ quantum electrons of charge -1 is $E(N,Z)=-{1/2}Z^2\ln Z+(E^{\TF}(\lambda)+{1/2}c^{\rm H})Z^2+o(Z^2)$ when $Z\to \infty$ and $N/Z\to \lambda$, where $E^{\TF}(\lambda)$ is given by a Thomas-Fermi type variational problem and $c^{\rm H}\approx -2.2339$ is an explicit constant. We also show that the radius of a two-dimensional neutral atom is unbounded when $Z\to \infty$, which is contrary to the expected behavior of three-dimensional atoms.

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